Answered: e. 8 b(dv(b←d)) (d~←b_)↔(b←d) '…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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4. Write each statement in symbolic form, and use truth tables to determine if they are logically equivalent: (define any variables you use) A: If you study hard and do all homework, then you will pass the class. B: If you study hard and did not pass the class, then you did not do all your homework.
Are the following expressions logically equivalent? (present a truthtable)~p ⋁ ~q ⋁ ~ r ; ~ (p ⋀ r ⋀ q)
2. Let p, q andr be the following statements: p: You run 10 laps daily. q: You are healthy. r: You take multi-vitamins. Translate the following into logical notation using p, q and r as logical connectives. a) You run 10 laps daily, you take multi-vitamins, and you are healthy. b) Either you are healthy or you do not run 10 laps daily, and you do not take multi-vitamins. c) If you do not run 10 laps daily or do not take multi-vitamins, then you will not be healthy.
Determine whether the logical statement is a tautology, a contradiction or neither: (p→q) → (p v q). [Hint: Use a truth table with 4 rows; you need to check the last row; all T is a tautology: all F is a contradition; a mixture of T and F is neither.] Example statement: If adopting new software leads to savings, then we'll either adopt new software or save money. The parentheses fit in the statement like this: If (adopting new software leads to savings), then (we'll either adopt new software or save money). This interpretation gives adopting new software leads to savings = If we adopt new software, then we'll save money O a. Tautology O b. Neither Oc. Contradiction
For each logical argument, select all the truth assignments for the propositional variables that show the logical argument is invalid. 1) 2) r S T T r T F T F p+ -q rv ¬S FT F T :- F F F F
b) Determine if the statement below is true or false, and explain your reasoning. If two statements are logically equivalent, then so are their negations.

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e. 8 b(dv(b←d)) (d~←b_)↔(b←d) ' (bnd)v(b_vd)